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The vortex particle method (VPM) is a mesh-free approach to computationalfluid dynamics (CFD) solving the Navier-Stokes equations in theirvelocity-vorticity form. The VPM uses a Lagrangian scheme, which not onlyavoids the hurdles of mesh generation, but it also conserves vorticalstructures over long distances with minimal numerical dissipation while beingorders of magnitude faster than conventional mesh-based CFD. However, VPM isknown to be numerically unstable when vortical structures break down close tothe turbulent regime. In this study, we reformulate the VPM as a large eddysimulation (LES) in a scheme that is numerically stable, without increasing itscomputational cost. A new set of VPM governing equations are derived from theLES-filtered Navier-Stokes equations. The new equations reinforce conservationof mass and angular momentum by reshaping the vortex elements subject to vortexstretching. In addition to the VPM reformulation, a new anisotropic dynamicmodel of subfilter-scale (SFS) vortex stretching is developed. This SFS modelis well suited for turbulent flows with coherent vortical structures where thepredominant cascade mechanism is vortex stretching. Advection, viscousdiffusion, and vortex stretching are validated through simulation of isolatedand leapfrogging vortex rings. Mean and fluctuating components of turbulentflow are validated through simulation of a turbulent round jet, where Reynoldsstresses are resolved directly and compared to experimental measurements.Finally, the computational efficiency of the scheme is showcased in thesimulation of an aircraft rotor in hover, showing our meshless LES to be 100xfaster than a mesh-based LES with similar fidelity, while being 10x faster thana low-fidelity unsteady Reynolds-average Navier-Stokes simulation and 1000xfaster than a high-fidelity detached-eddy simulation.

Reviving the Vortex Particle Method: A Stable Formulation for Meshless Large Eddy Simulation